Minimum length high quality differential pressure producing flow meter

ABSTRACT

The disclosure concerns fluid flow metering devices of the differential pressure producing type comprising a tube which defines a throat and a converging section for guiding fluid thereto from an inlet region of larger cross section. The tube has a special converging section which accelerates the fluid at two different rates and causes it to form two vena contractas before it reaches a true static pressure tap in the throat. The tube is designed in accordance with specified dimensional relationships which provide a tube of minimum length preferably having a discharge coefficient of 0.98 and a &#39;&#39;&#39;&#39;2 sigma&#39;&#39;&#39;&#39; accuracy tolerance between + OR - 0.5 percent and + OR - 1 percent depending upon whether the tube has a circular or a polygonal cross section.

United States Patent [1 1 Halmi [111 3,733,902 1 May 22,1973

[75] Inventor: Dezsoe Halmi,Cranston,R.I.

[73] Assignee: General Signal Corporation, Rochester, NY.

[22] Filed: Aug. 9, 1972 [21] Appl. No.: 279,154

Related US. Application Data [63] Continuation-impart of Ser. No.144,898, May 19,

I 1971, abandoned.

[52] US. Cl ..73/2l3, 138/44 [51] Int. Cl. ..G01f 1/00 [58] Field ofSearch ..73/2l3; 138/44 [56] References Cited UNITED STATES PATENTS1,850,030 3/1932 Pardoe ..73/213 2,704,555 3/1955 Dali 2,868,013 l/1959Terrell ..73/2l3 Q b w C OTHER PUBLICATIONS R. G. West, Rectangular TubeDesign, Instrument Practice December 1961, p. 1547-1552 PrimaryExaminer-Richard C. Queisser Ass stan Eaq nin t-rl n B sqshami? V 7Attorney.leffrey S. Mednick and Milton E. Kleinman [57] ABSTRACT Thedisclosure concerns fluid flow metering devices of the differentialpressure producing type comprising a tube which defines a throat and aconverging section for guiding fluid thereto from an inlet region oflarger cross section. The tube has a special converging section whichaccelerates the fluid at two different rates and causes it to form twovena contractas before it reaches a true static pressure tap in thethroat. The tube is designed in accordance with specified dimensionalrelationships which provide a tube of minimum length preferably having adischarge coefficient of 0.98 and a 2 sigma" accuracy tolerance between:0.5 percent and :1 percent depending upon whether the tube has acircular or a polygonal cross section.

PATENTEBH-XZZISB INVENTOR DEZSOE HALMI BY (A 2213/ p0,? 9/ ATTORNEYS 1MINIMUM LENGTH HIGH QUALITY DIFFERENTIAL PRESSURE PRODUCING FLOW METERDESCRIPTION OF ILLUSTRATED EMBODIMENTS The embodiment of the inventionshown in FIGS. 1

CROSS'REFERENCE To RELATED APPLICATION and 2 employs a tube 11 ofcircular cross section which This application is a continuation-in-partof U. S. application Ser. No. 144,898, filed May 19, 1971, nowabandoned.

BACKGROUND AND SUMMARY OF THE INVENTION Application Ser. No. 48,341,filed June 22, 1970, now U.S. Pat. No. 3,686,946, discloses a highquality flow meter of the differential pressure producing type whichcomprises a throat, and a converging section which guides fluid theretofrom an inlet region of larger cross section. This instrument ischaracterized by internal geometry which causes the accelerating fluidto form one vena contracta in the converging section and a second venacontracta at the throat entrance, and by the use of a pressure tap inthe throat which senses true static pressure at a point where the flowis attached to the tube wall. The tube, which has a circular crosssection, affords a discharge coefficient on the order of 0.98, and 2sigma accuracy tolerances of 10.5 percent and 10.75percent,,respectively, for Beta ratios below and above 0.55. ApplicationSer. No. 144, 802, filed on May 19, 1971 now abandoned, extends theseteachings and presents a high quality differential producer having apolygonal, normally rectangular, cross section which affords a closelycomparable discharge coefficient and a 2 'sigma accuracy tolerance of i1percent over the whole range of useful Beta ratios (i.e., ratios between0.75 and 0.3).

The object of the present invention is to provide minimum lengthversions of the high quality instruments disclosed in the aforementionedapplications. The invention furnishes a set of empirically determinedrelationships which are valid for both circular and polygonalinstruments, and which specify the minimum dimensions for the criticaltube portions in terms of the cross sectional area of the inlet or thethroat-and the Beta ratio. The set includes the relationships requiredfor the basic meter, which consists of the converging section, thethroat and the throat tap, as well as the relationships needed for tubesof the flange ended type which include an inlet section containing astatic pressure tap, and those which include a diffuser or head recoverysection.

herein with reference to the accompanying drawing in Y which:

FIG. 1 is a horizontal, axial sectional view, in schematic form, of aflange ended tube having a circular cross section.

FIG. 2 is a sectional view taken on line 2-2 of FIG. 1.

FIG. 3 is a horizontal, axial sectional view, in schematic form, of aflange ended tube having a rectangular cross section.

FIG. 4 is a sectional view taken on line 4--4 of FIG. 3.

includes cylindrical inlet and throat sections 12 and 13, respectively,a converging section 14 consisting of conical portions 15 and 16, and aconical diffuser 17. Conical portion 16 intersects portion 15 and throat13 along continuous edges 18 and 19, respectively, therefore, as fluidflowing through tube 11 forms one vena contracta as it leaves portion15, reattaches to the tube wall in portion 16, forms a second venacontracta as it leaves this portion, and then reattaches to the wall ofthroat 13. the upstream portion 15 of converging section 14 has thegreater cone angle, so the vena contracta produced at edge 18 is morepronounced than the one produced at edge 19. As explained in applicationSer. No. 48,341, now US. Pat. No. 3,686,946, these vena contractasnormalize the flow pattern (i.e., the velocity distribution acrosstheflowing stream), and thereby tend to make the discharge coefficientof tube 1 1 insensitive to changes in the design and condition of theupstream ducting.

Inlet and throat sections 12 and 13 are equipped with pressure taps 21and 22 which are constructed in the conventional manner, but arepositioned to sense the true static pressures in these sections. Inother words, each tap senses pressure in a region where the flow isattached to the tube wall.

The axial dimensions a-g shown in FIG. 1, for a 2 sigma accuracy of $0.5percent, are determined from the following formulas, wherein A,and A arethe cross sectional areas of inlet and throat sections 12 and 13,respectively, and B is the Beta ratio of the tube (i.e., the ratio ofthe square roots of the cross sectional areasof the throat and theinlet):

a from approximately 1 inch to infinity proximately 1.l VAZI.67-0.76B)

d from approximately 0.5 VA? to approximately 0.6 VA e f fromapproximately 0.3 VA: to 0.9 VA: 8 up to 6 VAHO-78 \K fl-78 Thesefon'nulas together with the cross sectional area of the tube at edge 18,which is determined from the expression 1.15 A completely define theinternal shape of tube 11, and result in a tube having the minimumlength needed to achieve the superior performance described inapplication Ser. No. 48,341, now US. Pat. No. 3,686,946. Moreover, sinceall of the critical relationships are expressed in terms dependent uponline size and differential pressure requirements, the invention providesthe optimum tube for any particular application which may beencountered.

For a 2 sigma accuracy of i 4.5 percent the following formulas are inorder:

a from approximately 1 inch to infinity formulas are in order: a fromapproximately 1 inch to infinity b from approximately 0.28 VA,(B0.31) toapproximately 2.0 \/A,(B0.3 l)

d from approximately 0.3

e f from approximately 0.2

mately 0.7 VA

g up to 6 /A,,0.'7 VA 0.78

The embodiment shown in FIGS. 3 and 4 also is constructed in accordancewith the formulas given above, but here the tube 11a has a rectangularcross section defined by upper and lower parallel walls 23 and 24,respectively, and a pair of identical, shaped side walls 25 and 26 whichdefine inlet section 12a and throat 13a are parallel. Although, in thecase of the first embodiment, the circumferential position of the taps21 and 22 is immaterial, in the rectangular version it is necessary, forbest results, to locate the tabs 21a and 22a in one of the shaped sidewalls 25 and 26, and to position them midway between the top and bottomwalls (see FIG. 4). The performances of the two embodiments are closelycomparable, but the rectangular tube 11a has a slightly larger 2 sigmaaccuracy approximately 0.5 percent greater than that for a circulartube.

Either embodiment of the invention may take the form of an insert tube,in which case inlet section 12 or 12a is omitted, and the inlet tap 21or 21a may be replaced by a corner tap. However, since the insert typeof tube does not perform as well as the flange ended type, it is notrecommended for applications where precise flow measurements arerequired. In applications where head recovery is not important, thediffuser 17 or 17a may be omitted without adversely affecting themetering accuracy of the tube.

While there has been described what is at present considered to be thepreferred embodiment of the invention, it will be obvious to thoseskilled in the art that various changes and modifications may be madetherein without departing from the invention, and it is, therefore,aimed in the appended claims to cover all such changes and modificationsas fall within the true spirit and scope of the invention.

What is claimed is:

1. A flow metering device of the differential pressure producing typecomprising a. a tube which-defines a throat and a converging sectionwhich guides fluid thereto from an inlet region of larger cross section,

b. the converging section having adjoining upstream and downstreamportions which accelerate the fluid at different rates and each of whichhas an edge at its exit end which causes the fluid to form a venacontracta,

c. the axial length of the upstream portion being between 0.5 m(0.67-0.768) and 2.0 VAT (0.67-0.768) and the axial length of thedownstream portion being between 0.3 \/K; and 0.9

VA to approximately- VA; to approxim, and the axial length of the throatbeing between 0.4 VK; and 1.4 VA; where A, and A are the cross sectionalareas of the inlet region and the throat, respectively, and B is theBeta ratio of the tube; and

d. a true static pressure tap located in the middle of the throat.

2. A flow metering device as defined in claim 1 in which the axiallength of the upstream portion is between VA;(0.670.76B) and 1.1\/K,(0.67-0.76B) and the axial length of the downstream portion isbetween 0.5 VA; and 0.6 VA;

3. A flow metering device as defined in claim 2 in which a. the tubealso defines an inlet section which is joined to the throat by theconverging section; and

b. the inlet section contains a true static pressure tap spaced axiallyfrom the entrance of the converging section a distance between 0.28 VA,(B0.3l) and 2.0 VA, (B0.31).

4. A flow metering device as defined in claim 3 in which the tap is atleast 1 inch from the entrance of the inlet section. I

5. A flow metering device as defined in claim 1 in which the tube alsodefines a diffuser joined to the exit end of the throat and having anaxial length up to (6 VAT 0:73 VA ,0.78).

6. A flow metering device as defined in claim 3 in which the tube alsodefines a diffuser joined to the exit end of the throat and having anaxial length up to (6 7. A flow metering device as defined in claim 4 inwhich the tube also defines a diffuser joined to the exit end of thethroat and having an axial length up to (6 8. A flow metering device asdefined in claim 7 in which a. the tube hasa circular cross section;

b. the inlet section and the throat are cylindrical; and I c. the twoportions-of the converging section and the difiuser are conical. 9. Aflow metering device as defined in claim 7 in which a. the tube has arectangular cross section; and b. each of the taps is located in a tubewall having a portion in.the converging section which changes directionof flow. v 10. A flow metering device as defined in claim 9 in which a.the tube comprises two parallel walls and two shaped walls; and

b. the taps are located in one of the shaped walls. t! i 8K I I UNITEDSTATES PATENT OFFICE CERTIFICATE OF CORRECTION 'Patent No. 3,733,902Dated 22, 1973 Dezsoe Halmi Inventor(s) It is certified that errorappears in the above-identifiedpatent and that said Letters Patent arehereby corrected as shown below:

I Column 2,. 1i n es 42 and 43 should appear as shown below:

I c= from approximately (0.67-0.76B) *to approximately 1.1 \TIF'(0.67-0.76B)

' Sigfied "and sealed this 20th day of August 1974.

Attest: I v

MCCOY M. GIBSON,-. JR. Y c. MARSHALL DANN Attesting Officer 1Commissioner of Patents FORM PO-IOSO (10 69) USCOWWDC 37 P69 a u.s,eovznunsur PRINTING OFFICE l9" o-ase-aan.

UNITED rams PATENT errrer @ERTEFEQATE @F C URREQCTEQN Patent No. 3 733902 Dated May 22, 1973 Inventm-(S) De 2 soe Halmi It is certified thaterror appears in the above-identified patent and that said LettersPatent are hereby corrected as shown below:

On column 2, cancel lines l q-Lt? and substitute the 1 followingtherefor:

I to approximately 0.6 A v e f from approximately 0.3 i A toapproximately 0.9 A

On column 2, lines 66 and 67 (two occurrences) replace FORM P0-1050(10-69) uscoMM-Dc 60376-P69 6 5 i U.S GOVERNMENT PRINTING OFFICE I919O-3SG-334,

UNITED STATES PATENT OFFICE Page 2 CERTIFICATE U QORREGEWN Patent N3,733,902 Dated y 973 Inventor( 250e Halmi It is certified that errorappears in the above-identified patent and that said Letters Patent arehereby corrected as shown below:

In column L lines 26 and 27, 30 and 31, and 3). and 35 each occurrencereplace A A A -A I- I T H l l' J0.78 Jams} J0.78 I JO.

Signed and sealed this 26th day of February 1971 (SEAL) Attest:

EDWARD M.FLETCHER,JH.

C. MARSHALL DANN Attestlng offlcer Commissioner of Patents FORM PO-IOSO(10-69) uscoMM-oc 60376-P69 U,S. GOVERNMENT PRINTING OFFICE l9,O-QGi-Sll,

1. A flow metering device of the differential pressure producing typecomprising a. a tube which defines a throat and a converging sectionwhich guides fluid thereto from an inlet region of larger cross section,b. the converging section having adjoining upstream and downstreamportions which accelerate the fluid at different rates and each of whichhas an edge at its exit end which causes the fluid to form a venacontracta, c. the axial length of the upstream portion being between 0.5square root AI (0.67-0.76B) and 2.0 square root AI (0.670.76B) and theaxial length of the downstream portion being between 0.3 square root ATand 0.9 square root AT, and the axial length of the throat being between0.4 square root AT and 1.4 square root AT, where AI and AT are the crosssectional areas of the inlet region and the throat, respectively, and Bis the Beta ratio of the tube; and d. a true static pressure tap locatedin the middle of the throat.
 2. A flow metering device as defined inclaim 1 in which the axial length of the upstream portion is betweenSquare Root AI (0.67-0.76B) and 1.1 Square Root AI(0.67-0.76B) and theaxial length of the downstream portion is between 0.5 Square Root AT and0.6 Square Root AT.
 3. A flow metering device as defined in claim 2 inwhich a. the tube also defines an inlet section which is joined to thethroat by the converging section; and b. the inlet section contains atrue static pressure tap spaced axially from the entrance of theconverging section a distance between 0.28 Square Root AI (B-0.31) and2.0 Square Root AI (B-0.31).
 4. A flow metering device as defined inclaim 3 in which the tap is at least 1 inch from the entrance of theinlet section.
 5. A flow metering device as defined in claim 1 in whichthe tube also defines a diffuser joined to the exit end of the throatand having an axial length up to (6 Square Root AI/0.78 - Square RootAT/0.78).
 6. A flow metering device as defined in claim 3 in which thetube also defines a diffuser joined to the exit end of the throat andhaving an axial length up to (6 Square Root AI/0.78 - Square RootAT/0.78).
 7. A flow metering device as defined in claim 4 in which thetube also defines a diffuser joined to the exit end of the throat andhaving an axial length up to (6 Square Root AI/0.78 - Square RootAT/0.78).
 8. A flow metering device as defined in claim 7 in which a.the tube has a circular cross section; b. the inlet section and thethroat are cylindrical; and c. the two portions of the convergingsection and the diffuser are conical.
 9. A flow metering device asdefined in claim 7 in which a. the tube has a rectangular cross section;and b. each of the taps is located in a tube wall having a portion inthe converging section which changes direction of flow.
 10. A flowmetering device as defined in claim 9 in which a. the tube comprises twoparallel walls and two shaped walls; and b. the taps are located in oneof the shaped walls.